In this paper, the main subharmonic resonance of the Mathieu–Duffing system with a quintic oscillator under simple harmonic excitation, the route to chaos, and the bifurcation of the system under the influence of different parameters is studied. The amplitude-frequency and phase-frequency response equations of the main resonance of the system are determined by the harmonic balance method. The amplitude-frequency and phase-frequency response equations of the steady solution to the system under the combined action of parametric excitation and forced excitation are obtained by using the average method, and the stability conditions of the steady solution are obtained based on Lyapunov's first method. The necessary conditions for heteroclinic orbit cross section intersection and chaos of the system are given by the Melnikov method. Based on the separation of fast and slow variables, the bifurcation phenomena of the system under different conditions are obtained. The amplitude-frequency characteristics of the total response of the system under different excitation frequencies are investigated by analytical and numerical methods, respectively, which shows that the two methods achieve consistency in the trend. The influence of fractional order and fractional derivative term coefficient on the amplitude-frequency response of the main resonance of the system is analyzed. The effects of nonlinear stiffness coefficient, parametric excitation term coefficient, and fractional order on the amplitude-frequency response of subharmonic resonance are discussed. Through analysis, it is found that the existence of parametric excitation will cause the subharmonic resonance of the Mathieu–Duffing oscillator to jump. Finally, the subcritical and supercritical fork bifurcations of the system caused by different parameter changes are studied. Through analysis, it is known that the parametric excitation coefficient causes subcritical fork bifurcations and fractional order causes supercritical fork bifurcations.

In this paper, the profile of the bar is detected by laser vision technology. During the detection process, obvious isolated outliers can be observed in the profile data; dimension parameter and profile-fitting accuracy are seriously affected by these outliers. In order to eliminate these outliers and improve the measurement accuracy, this paper uses Hampel identifier and moving mean identifier to identify isolated outliers. At the same time, the profile data is fitted, and the fitting results and fitting accuracy were analyzed and compared between the original data and the renovated data. The experiment proves that the outliers in the data must be identified and processed in the data measurement process. The Hampel identifier has better recognition effect, its algorithm is simple, efficient, and robust, and it can play an important role in the preprocessing of profile data based on structured light.